Abstract
Three phase induction motor plays major role in our daily life. This paper deals with optimal design and analysis of a 3-phase induction machine that is very suitable for industrial application. Calculation of the shape of rotor, end ring current, slot dimension, air gap length is main design goal. A standard machine designed in auto cad and two different models are obtained by changing the shape of rotor slots and simulate in FEMM. Comparing the simulation results are gives the effective and optimal designed.
Introduction
A poly phase induction motor is a single excited ac machine.
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Its stator winding directly connected to ac source, whereas rotor winding receives its energy by means of mutual action. The stator is formed by connecting distributed coil. In designed aspect there are lots of parameters on which, the performance of induction motor is noticeably changed. These parameters are shape and size of stator/rotor slots, stator/rotor winding, air gap, no. of turns, end ring etc.
Again basically there are two types of major fault occurs in induction machine i.e. electrical and mechanical fault. Electrical fault mainly consists of overvoltage/under voltage fault. Mechanical fault due to broken of rotor bar, bearing fault etc.
The 3-phase induction motor having specification- ‘3-phase 415 volt, 50Hz, 1425 rpm, star connected, 4-pole is chosen’. The aim of this paper is designed a model of induction motor and investigate the optimum motor model parameters when the materials are changed.
Design Methodology
The design process encompasses both hydraulic and engineering aspects, aiming for an economically viable yet high-performing motor.
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Key parameters such as synchronous speed, stator core diameter, specific loading, efficiency, and power factor are calculated to determine the motor's main dimensions. The design emphasizes reducing friction losses and optimizing both pressure and flow velocities within the system.
Main dimension
Synchronous speed ns = 1500 rpm
Number of pole = 4
From Table No – 1 recommended value of specific loading
Stator core diameter = 0.1 m
Bav = 0.3 Wb/m2
ac = 11000 A/m
Current density (δ) = 4 Amp/m2
From Table No – 2 Efficiency and power factor
Output = 0.75 kw
No of pole = 4
Efficiency = 0.72
Power factor = 0.75
KVA Output = Q = kw/ηCosɸ = 0.75/0.72*0.75 = 1.388
Output coefficient = Co = 11*Kw*Bav*ac*10-3
Kw = 0.955 winding factor is assumed 0.955 in the value of winding factor for infinitely distributed winding with full pitch coil.
Co = 11*0.955*0.3*11000*10-3 = 34.66
Synchronous speed = ns = 2f/P = 25 rps
Q = CoD2Lns
D2L = Q/Cons = 1.388/34.66*25 = 1.601*10-3 m3
For economical design, L/τratio = 1.5 taking
L/τ= 1.5
L/(πD/P) = 1.5
L = 1.18 D
So, D2L = 1.601*10-3
1.18 D3 = 1.601*10-3
D3 = 1.356*10-3
D = 0.110 m , L = 1.18*0.110 = 0.13 m
Stacking Factor = 0.9
Net iron length = 0.9*0.13 = 0.117 m
Stator Designed and Calculation
Pole pitch (τ) = (πD)/P = π*0.11/4 = 0.086 m
Flux per pole (ɸm) = BavLτ= 0.3*0.13*0.086 = 3.354*10-3 Wb
Stator per phase voltage = 415/√3 = 239.6 volt
Stator turns per phase (Ts) = 239.6/(4.44fɸmKw) = 239.6/ (4.44*50*3.354*10-3*0.955) = 336.95
It is a good practice to use as many slots as economically possible.However no of slots per pole per phase q, should not be less than 2, otherwise leakage reactance is more high.
Q = 2
Ss/mp = 2
Total no of stator slots (Ss) = 2 mp = 24
Slot pitch (Ys) = πD/Ss=14.3 m
Total no of stator conductor = 6 Ts = 6*336 = 2016
Conductor per slots (Zss) = 2016/24 = 84
It is a small size machine & since semi enclosed slot are used for this machine,the slot pitch can be lower than 15 mm, however mechanical reason slot pitch should not below 10 mm mush winding in tapered semi enclosed slot is used for stator the machine winding is single layer & total no of stator coil is equal to half the no of stator slot.
24/2 = 12
Coil span = S/P = 24/4 = 6
But slot winding should not be even integer in case mush winding therefore a coil span S is used.
The coils are wounded by slot pitch.
Angle of chording (α) = 180˚/6 = 30˚
r = 180˚/(S/P) = 30˚
Pitch factor Kp = cos (α/2)˚ = 0.9659
Distribution factor Kd = Sin (qr/2)/q sin (r/2) = Sin (60/2)/2 sin (30/2) = 0.9659
Stator winding factor (Kws) = Kp * Kd = 0.9659*0.9659 = 0.9329
Stator line current Is = 0.75*10-3/(√3*415*0.72*0.75) = 1.932 Amp
Current density = 4A/mm2
Area of stator conductor required = 1.932/4 = 0.48305 mm2
Diameter of conductor bare required (π/4)d2 = 0.48305
d = 0.78 mm
From Table No – 3 Round copper wire synthetic enamel
Nearest bare conductor diameter (d) = 0.80 mm
Area of stator conductor as = (π/4)*0.82 = 0.50265 mm2
Current density of stator conductor = δs = 1.932/as = 1.932/0.50265 = 3.84 A/mm2
Diameter of enamelled conductor (d1) = 0.884 mm (using medium covering)
Slot Dimension
Space required for bare conductor in a slot
Zss * as = 84*0.50265 = 42.28 mm2
Taking a space factor of 0.4 for the slots
Area of each slots = 42.28/0.4 = 105.71 mm2
Before deciding the slot dimensions to give the above area, the minimum tooth width that would keep the flux density within limits must be found the maximum allowable flux density is 1.7 Wb/m2.
Minimum width of stator teeth = Wts = ɸm/(1.7*(Ss/P)*L1 = 3.354*10-3/1.7*(24/4)*0.117 = 2.81 * 10-3 = 2.81 mm
A tooth of constant width 5.0 mm is taken.
Take lip = 1.5 mm and wedge = 3.5 mm
Let, nv = no of conductors vertically
nh = no of conductors horizontally
So, Zss = nv * nh
nv / nh = 3 → 5
Solving (1) & (2) we get,
84 = nv * nh = 4nh * nh
nh2 = 21
nh = 4.58 ≈ 5
nv = 84/5 = 16.8 =17
Height of slot, hs1 = (nv * dc + 3*0.5+3.5+1.5+2) mm = 23.5 mm
Width of slots, bs1 = (nh * dc + 2*0.5+2) mm = 7.42 mm
Slot opening, bo1 = (2/5) bs1 = 2.9668 mm
Rotation, hs1/bs1 = 3 → 5
Stator Teeth
Flux density in stator teeth = ɸm/ (Ss/P) * Wts * L1 = 3.354 * 10-3/(24/4)*6*10-3*0.117
= 0.796 Wb/m2 ≈ 0.8 Wb/m2
A high value of flux density in the teeth is not desirable, as it leads to a higher iron loss and a greater magnetizing mmf. As stated earlier, the maximum value of Bts, the mean flux density in stator teeth should not exceed 1.7 Wb/m2.
Rotor Designed and Calculation
Air Gap
Air gap length (lg) = 0.2 + 2√(DL) = 0.2 + 2√(0.11*0.13) = 0.439 ≈ 0.44 mm
But this would cause high result in large magnetizing current and therefore a shorter gap should be used.
Air gap length 0.3 mm
Diameter of rotor (Dr) = 110-(2*0.3) = 109.4 mm
The number of motor slots taken as 1 pole pair (4/2) = 2 smaller than stator slots.
Ss = 24, Sr = 23
Rotor slot pitch (Ysr) = (π * 0.1094)/24 = 0.01562 m = 15.62 mm
Rotor bar current (Ib) = (2ms*Kws*Ts)/Sr*IsCosɸ = (2*3*0.9329*336)/23*(1.932*0.75)
= 118.48 amp
In order to obtained a good starting torque a high value of current density should be used for rotor bar.
Taking rotor bar current density 3 amp/m2
ab = 118.48/3 = 39.49 mm2
As per Table No – 4Recommended sizes of copper strip IS 1897-1962 (7*6) mm2 with an area
Wsr = Width of rotor slot = 6.3 mm
Depth of rotor slot = 9.3 mm
Slot pitch at bottom of slot = π (109.4-2*9.3)/23 = 12.40 mm
Total width at the bottom side Wt = 12.40-6.3 = 6.10 mm
Flux density of rotor teeth = ɸm/(23/4)*0.13*3.28*10-3 = 3.354*10-3/(23/4)*0.13*3.28*10-3 =0.0735 Wb/m2
The bars are skewed by one slot pitch.
Extending the bar 15 mm beyond the each core 10 mm each side.
Length of each bar = 130 + (2*15) + 10 = 170 mm
Rb = ρL/A = 0.021*0.17/42 = 85*10-6 Ω
Total loss in bar = 23*(118.48)2*85*10-6 = 27.44 Watt
Order of slots harmonics = n = 2Ss/P ± 1 = 2*(24/4) ± 1 = 13,11
In order to complete eliminate the 13th order harmonics.
Angle of skewing = 720/ (n*P) = 720/ (11*4) = 16.36˚ mech
Or, Angle of skewing = 720/ (13*4) = 13.84˚ mech
Rotor End Ring Calculation
The rotor bars are permanently shorted with the help of end rings.
End ring current Ic = (Ss * Ib) / (π * P) = (23*118.48)/(π * 4) = 216.85 Amp
Taking current density 3A/m2
Area of end ring = 216.85/3 = 72.28 mm2
Using a ring of 10*8 mm section
Depth of ring de = 10 mm
Thickness of ring = 8 mm
And area of end ring ae = 80 mm2
The ring is brazed to the bars.
In practice, however, the rotor of this machine may be die cast using aluminium.
Outer diameter of end ring = 109.4 – (2*9.3) = 90.8 mm
Inner diameter of end ring = 90.8 – (2*10) = 70.8 mm
Mean diameter of end ring (Dc) = 80.8 mm
Resistance of each end ring (re) = (ρπDe)/ae = (0.021*π*80.8*10-3)/80 = 66.63 * 10-6 Ω
Copper loss in two end rings = 2*Ie2*re = 2*(216.85)2*66.63*10-6 = 6.26 Watt
Total copper loss = 6.26 + 27.44 = 33.7 Watt
33.7/750 = 0.044 S/(1 – S)
So, S = 0.042
Stator core
Length of mean turn = 2L + 2.3τ+ 0.24 = 2*0.13 + 2.3[(π*0.11)/4] + 0.24 = 0.698 mm
Flux in stator core = 3.354*10-3/2 = 1.677*10-3 Wb
Assume flux density 1.2 Wb/m2
Area of stator core Acs = 1.677*10-3/1.2 = 1.397*10-3 m2
Depth of the stator core = dcs = 1.397*10-3/0.117 = 11.94*10-3 ≈ 12 mm
Flux density at stator core Bcs = 11.94/12 * 1.2 = 1.194 Wb/m2
Outside diameter of stator laminatiom = D0 = D + 2dss + 2dcs = 110+2(23.5+18.5) = 194 mm
Rotor core
The value of depth of rotor core is taken equal to the value of stator core.
Depth of rotor core = dcr = 18.5 mm
Flux density in stator core = 1.194 Wb/m2
Inner diameter of rotor = Di = Dr – 2(dsr + dcr) = 109.4- 2(9.3+18.5) = 53.8 mm
Detailed calculations for the stator and rotor dimensions, including the pole pitch, flux per pole, stator turns per phase, slot dimensions, and air gap length, are presented. For the stator, a focus on slot pitch, coil span, winding factor, and current density reveals insights into achieving an efficient design. The rotor design includes considerations for air gap length, bar current, and end ring specifications, aiming for a balance between torque and current density. Simulations in FEMM validated the theoretical calculations, with adjustments made to the rotor slot shape enhancing performance.
Conclusion
The comparative analysis between two rotor slot shapes indicated that subtle changes in design could significantly impact motor performance. The optimized design achieved through AutoCAD and simulated in FEMM suggests a path forward for developing more efficient and reliable 3-phase induction motors suitable for industrial applications. This study underscores the importance of meticulous design and simulation in achieving an optimal induction motor model.
